Diane Abbott has revealed her staff try not to let her walk around her Hackney constituency alone after the murder of fellow Labour MP Jo Cox, as she called for parliament to consider launching an inquiry into racist and sexist abuse of MPs.

The shadow home secretary, who in 1987 became the first black woman to be elected as an MP, said she had been personally affected by the scale of abuse she has suffered, which reached a peak in recent weeks during a furore over which way she would vote on the government’s Brexit bill.

“When Jo Cox died, obviously my first thought was for her husband and children and friends and family and the people of Batley and Spen who lost a tremendous MP, but I also thought maybe you can’t shrug off these death threats any more. Maybe something could happen,” she told the Guardian’s political editor Anushka Asthana, presenting on LBC.

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“Since then I try not to walk around on my own any more. I don’t drive, I used to drive around Hackney on my own and I don’t do that any more and I’m getting new alarms and security on my house. It’s just a horrible atmosphere out there particularly if you are a woman MP and particularly if you’re a black MP.”

She later told Sky News programme Sophy Ridge on Sunday: “It kind of does get in your head, it kind of does demoralise you, and even though you know it shouldn’t, it does make you doubt yourself. It kind of does get in your head, it kind of does demoralise you, and even though you know it shouldn’t, it does make you doubt yourself.”

Abbott said people abusing her on the internet tended to dehumanise her and in particular “talk about black politicians in a different way”.

She called for Facebook and Twitter to do more to stop abuse being directed at people, while maintaining freedom of speech, and suggested a parliamentary inquiry could look into how the social media firms had responded to hate speech.

“No one really has a right to peddle this racist and sexist abuse … I think there is probably a case for a parliamentary inquiry, partly to make internet providers do more to close down these people,” she said.

“They are poisoning the political debate and putting off particularly young women from getting involved in political debate online and they must be putting off some women from getting involved in politics.”

Online abuse had become “turbo-charged”, Abbott said. “It’s it’s almost as if they want to drive some of us out of politics.

“Now you can press a button and threaten to rape someone. The more some of these guys see this stuff online, they more they become encouraged and emboldened.”

She said she first had a “wobble” about staying on as an MP a few years ago but was talked out of it by her colleague Keith Vaz who told her: “Diane, you have forgotten what it took for us to get here.”

Abbott first revealed the scale of abuse she received in an article for the Guardian last week, saying she might have thought twice about entering public life if she could have predicted some of the abuse she received today.

In the article, she said: “Suppose that someone had told me back then that 30 years on I would be receiving stuff like this: ‘Pathetic useless fat black piece of shit Abbott. Just a piece of pig shit pond slime who should be fucking hung (if they could find a tree big enough to take the fat bitch’s weight)’. Then I think that even the young, recklessly fearless Diane Abbott might have paused for thought.”

Abbott is one of a number of senior MPs to have spoken of the need to stop misogynistic abuse towards politicians in recent years, particularly online.

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Yvette Cooper, the former shadow home secretary, has said online harassment and abuse is “stifling debate and ruining lives”, while Maria Miller, the Tory former cabinet minister who now chairs parliament’s women and equality committee, has also called for action.

A number of online trolls have been convicted of threats towards female MPs, including two who subjected the Liverpool MP Luciana Berger to campaigns of antisemitic abuse. In 2014 a man was jailed for 18 weeks for bombarding the Labour MP Stella Creasy with messages threatening to rape her.

Jess Phillips, the MP for Birmingham Yardley, has spoken of receiving more than 600 threats of rape in one night on Twitter and had extra security installed in her home.